Calculate: {\text{begin}array l 5x+3y=7 } 4x+5y=3\text{end}array .

Expression: $\left\{\begin{array} { l } 5x+3y=7 \\ 4x+5y=3\end{array} \right.$

Multiply both sides of the equation by $5$

$\left\{\begin{array} { l } 25x+15y=35 \\ 4x+5y=3\end{array} \right.$

Multiply both sides of the equation by $-3$

$\left\{\begin{array} { l } 25x+15y=35 \\ -12x-15y=-9\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$13x=26$

Divide both sides of the equation by $13$

$x=2$

Substitute the given value of $x$ into the equation $4x+5y=3$

$4 \times 2+5y=3$

Solve the equation for $y$

$y=-1$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( 2, -1\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 5 \times 2+3 \times \left( -1 \right)=7 \\ 4 \times 2+5 \times \left( -1 \right)=3\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 7=7 \\ 3=3\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( 2, -1\right)$